Residue Number Systems: A New Paradigm to Datapath Optimization for Low-Power and High-Performance Digital Signal Processing Applications

Abstract

Residue Number System (RNS) is a non-weighted number system which was proposed by Garner back in 1959 to achieve fast implementation of addition, subtraction and multiplication operations in special-purpose computations. Unfortunately, RNS did not turn out as a popular alternative to two?s complement number system in those days. The rigidity of instruction set architectures of the market-dominant computers and microprocessors then has been the main barrier to sustain the development of RNS-based applications. In recent years, technological advancement in semiconductor technology has revived the interests to reconsider RNS for application-specific computing. There are at least two unique motivations which make RNS computations more attractive and applicable in modern digital signal processing applications. Firstly, the modular and distributive properties of RNS are used to achieve performance improvements especially in the emerging distributed and ubiquitous computing platforms such as cloud, wireless ad hoc networks, and applications which require tolerance against soft error. Secondly, energy efficiency becomes a key driver in the continual densification of complementary metal oxide semiconductor (CMOS) digital integrated circuits. The high degree of computational parallelism in RNS offers new degree of freedom to optimize energy performance, particularly for very long word length arithmetic such as those involved in the hardware implementation of cryptographic algorithms. Our aim in this paper is to show this revolution by discussing interesting development in RNS and foster the innovative use of RNS for more applications. Different applications of RNS are investigated to demonstrate how this unconventional number system can be leveraged to benefit their implementation.